I open the weekly puzzles, minimize each window to keep it, then minimize the "free weekly puzzle" window. This allows you to break the internet connection. As long as you don't completely close the "free weekly puzzle" window you can open any of the puzzle windows and work offline. At least you can on a Mac using Safari.

If I don't have time to finish a puzzle before the week ends, I just leave it and the free weekly puzzles window open on my computer. I have a constant internet connection, but it stays open even when the connection crashes. I use Windows and Internet Explorer... I did learn the hard way to leave both windows open - I closed a few puzzles before I realized they were somehow attached to the free weekly puzzles window! ah well...more fun to solve them again I guess...